This study aims to analyze the correlation of temperature and humidity based on climatological data from Kuningan, West Java province, Indonesia, using non-linear regression and numerical analysis using the bisection method. In studying the education curriculum in Indonesia, most of them have studied linear regression, but only within certain limits, namely linear and multiple. It is still rare for students to use non-linear regression in their analysis. This paper will explain the analysis using non-linear regression as a source of data and equations in numerical analysis so that it can be applied in the context of the numerical bisection method. As for data processing and numerical analysis, Microsoft Excel is used. The authors combined the two variables in the non-linear analysis and used geometric equations for the numerical quotient analysis. The author displays the results of numerical graphs and real-time data obtained from the source "Data access viewer NASA.

Alfaris, Lulut

Indah, Indah

Nasution, Budiman

Siagian, Ruben Cornelius

Sinaga, Goldberd Harmuda Duva

English

Jurnal FKIP Universitas Mataram (Fakultas Keguruan Dan Ilmu Pendidikan)

Volume 8 No. 2 December 2022  Jurnal Pendidikan Fisika dan Teknologi (JPFT)    238 Non-Linear Regresion And Bisection Method Numerical Analysis of Humidity And Temperature Relationships  Lulut Alfaris1, Ruben Cornelius Siagian2*, Budiman Nasution2, Goldbed Harmuda Duva Sinaga3, & Indah2 1Department of Marine Technology, Pangandaran Marine And Fisheries Polytechnic, Indonesia 2Department of Physics, Medan State University, Indonesia 3Physics Education Study Program, Universitas HKBP Nommensen, Indonesia *Corresponding Author: rubensiagian_17@mhs.unimed.ac.id  Received: 2 November 2022; Accepted: 7 December 2022; Published: 23 December 2022 DOI: http://dx.doi.org/10.29303/jpft.v8i2.4394        Abstract - This study aims to analyze the correlation of temperature and humidity based on climatological data from Kuningan, West Java province, Indonesia, using non-linear regression and numerical analysis using the bisection method. In studying the education curriculum in Indonesia, most of them have studied linear regression, but only within certain limits, namely linear and multiple. It is still rare for students to use non-linear regression in their analysis. This paper will explain the analysis using non-linear regression as a source of data and equations in numerical analysis so that it can be applied in the context of the numerical bisection method. As for data processing and numerical analysis, Microsoft Excel is used. The authors combined the two variables in the non-linear analysis and used geometric equations for the numerical quotient analysis. The author displays the results of numerical graphs and real-time data obtained from the source "Data access viewer NASA." Keywords: Non-Linear regresion; Bisection method; Numerical method. INTRODUCTION Regression analysis is a fundamental method in many research problems because it involves analyzing the variables to be studied. In research, of course, there is not only one variable but many variables in the analysis (Codau et al., 2015). In many variables, of course, a method is needed how to be able to correlate these variables so that they have a relationship. Mathematical equations are the cornerstone in the analysis of these many variables. The analysis has at least two variables, X and Y. The interpretation of non-linear relationships is fundamental in understanding statistical phenomena from physical data and understanding the world entirely in its analysis for several variables; regression analysis is needed, where its function involves many problems or phenomena in the scientific environment and non-scientific life. The variables X and Y have a relationship, where these two variables can be used as variables with a certain rank in the equation. Non-linear relationships are the basis for most physical and statistical phenomena, and their study is essential to understand the world around us fully. The least-square model in statistical data is an estimator in the non-linear regression of the parameters reviewed. Non-linear square serves to minimize the sum of squared errors (SSE). In general, the regression analysis can be divided into 2, namely, Linear and non-linear regression (Amemiya, 1983). Many people think that distinguishing linear and non-linear regression only looks at the curvature of the line, but this is not entirely true, where the data model can adjust to the line equation. In non-linear regression, there are many forms, but in this article, we will explain the non-linear regression of the geometric type. (Pesaran & Deaton, 1978) Variable analysis in this article is temperature and humidity. It has humidity in the air that contains water content (Crosdale Volume 8 No. 2 December 2022  Jurnal Pendidikan Fisika dan Teknologi (JPFT)    239 et al., 2008). The temperature at the location influences air humidity. In the correlation between humidity, it is directly proportional because the air with water content in it increases as the temperature increases (Roberts, 1960), so the location in the area under study will stretch due to the high temperature. The higher the temperature, the higher the humidity level at that location. In this article, the numerical analysis uses the bisection method (Ayyub & McCuen, 1995). The bisection method is an approximation method to find the roots of the given equation by repeatedly dividing the interval (Jumin et al., 2021). We can find solutions to non-linear roots of equations using the bisection method (Zhao et al., 2014). We can run the numerical bisection process by using several processes or iterations and dividing the data by two. In the process, the principle of bisection is removing things that do not contain roots and taking things that contain roots, so you get the smallest.  RESEARCH METHODS This study uses a numerical computational analysis method, where data is taken from real data taken on the open access NASA web, namely from; https://power.larc.nasa.gov/data-access-viewer/.  The data taken is a time series of temperature and humidity in the city of Kuningan, West Java province in 2021. In the analysis the data taken is 1 data per month, so you will get 12 temperature data and 12 humidity data. The variables are X and Y, where humidity is variable X, and temperature is variable Y. In the regression analysis, the data for the x and y variables will be stretched to obtain the logarithmic values for the x and y variables, which aims to obtain the geometric equation (Brook & Arnold, 2018). After obtaining the parabolic equation, it can be taken to be analyzed using numerical analysis, namely analysis for 2, or commonly called the bisection method. The bisection method can function to find root values, and can find error or error values that you want to take in the analysis. The data taken is as follows for variable x as humidity, and variable y as temperature, namely:    Table 1. Raw data of temperature and humidity Month Humidity (g/kg) Temperatur (0C) January 18,01 24,95 February 18,31 24,8 March 17,94 25,41 April 17,88 25,33 May 18,49 25,74 June 17,94 25,25 July 16,91 24,7 August 16,97 25,12 September 17,03 25,54 October 17,4 26,03 November 18,01 25,87 December 17,94 25,72 Sum 212,83 304,46 Source: https://power.larc.nasa.gov/data-access-viewer/ (NASA) Volume 8 No. 2 December 2022  Jurnal Pendidikan Fisika dan Teknologi (JPFT)    240 This data is nonlinear data, so if we plot the scatter, we will get random and abstract or irregular results. So that it is necessary to process the data with the help of additional tables or commonly called regression analysis to obtain the geometric equations. As for the geometric sales model, they are as follows: ˆ bY aX=  (1) In the non-linear geometric equation above, there are constants a and b, which we can find. Before we look we have to log both sides of the equation, namely: ˆlog log logY a b X= +  (2)  So from this equation, we can get:  ˆ ' ' 'Y a bX= +  (3) Or simply: log loglogiiy xa bn n = −      (4) And for b is: ( ) ( ) ( )( ) ( )22log log log loglog logi i i ii in y x x ybn x x − =−    (5)  After we get the values of a and b, then we can substitute these values into equation (1), for numerical analysis using the bisection method. The algorithm in the bisection method in this article is: (a) estimating the values of a and b, where for f(a)*f(b)<0, (b) then for the second step we can find the roots of the equation, using the c rule = (a+b)/2, if we get the value of c, then we can calculate f(c). (c) evaluate using IF logic, where <f(a)*f(c)<0, then b=c, continue to the next step>, <f(a)*f(c)>0, then a=c , continue to the next step>, <f(a)*f(c)=0, stop iteration>.  RESULTS AND DISCUSSION The Figure 1 is the raw data correlation relationship between temperature and humidity, year 2021 in 12 months, in Kuningan City, West Java Province, Indonesia.  Figure 1. Time-dependent correlation of temperature and humidity raw data Based on non-linear regression analysis using equations (1), (4), and (5) by describing additional data tables in the form of logarithms, the result is that log a = 1.280737032, so that a is 11.87407184, while for the constant value b is obtained Volume 8 No. 2 December 2022  Jurnal Pendidikan Fisika dan Teknologi (JPFT)    241 0.098949483. We can plot a and b into geometric equations as in equation (1), so we have obtained a geometric equation for the temperature and humidity correlations for the city of Kuningan in 2021, which is equal to the following equation. 0,009894948311,87407184Y X=  (6) Furthermore, if we have obtained the equation, then we may analyze the equation using the numerical bisection method First of all we need to prepare the head table for inputting numeric data, which is like in the picture above. Next, input the value of a with 1, we enter b with 2 as the final limit in the analysis of the roots of the equation. For c is the middle value of a and b, in numeric excel it can be written as =(B26+C26)/2 . We can input it into the function by substituting a, b, and c into equation (6), so we get: Table 2. Scroll down after entering the logical if in the columni a b c f(a) f(b) f(c) eror (ɛ) 1 1 2 0 11,87407184 12,71705163 12,36015199 0 2 1,5 2 1,75 12,36015199 12,71705163 12,55012818 0,142857 For machine programs in Exel to run as they should, then we can provide logic to Exel, namely evaluate using IF logic, where <f(a)*f(c)<0, then b=c, continue with the next step>, < f(a)*f(c)>0, then a=c, continue to the next step>, <f(a)*f(c)=0, stop iteration>. Next we may iterate until the iteration iteration for error is 0. as  Table 3. Numerical bisection method analysisi a b c f(a) f(b) f(c) eror (ɛ) 1 1 2 0 11,87407184 12,71705163 12,36015199 0 2 1,5 2 1,75 12,36015199 12,71705163 12,55012818 0,142857 3 1,75 2 1,875 12,55012818 12,71705163 12,63609862 0,066667 4 1,875 2 1,9375 12,63609862 12,71705163 12,67716348 0,032258 5 1,9375 2 1,96875 12,67716348 12,71705163 12,69725019 0,015873 6 1,96875 2 1,984375 12,69725019 12,71705163 12,70718603 0,007874 7 1,984375 2 1,9921875 12,70718603 12,71705163 12,71212755 0,003922 8 1,9921875 2 1,99609375 12,71212755 12,71705163 12,71459176 0,001957 9 1,99609375 2 1,99804688 12,71459176 12,71705163 12,71582224 0,000978 10 1,99804688 2 1,99902344 12,71582224 12,71705163 12,71643707 0,000489 11 1,99902344 2 1,99951172 12,71643707 12,71705163 12,71674439 0,000244 12 1,99951172 2 1,99975586 12,71674439 12,71705163 12,71689802 0,000122 13 1,99975586 2 1,99987793 12,71689802 12,71705163 12,71697483 6,1E-05 14 1,99987793 2 1,99993896 12,71697483 12,71705163 12,71701323 3,05E-05 15 1,99993896 2 1,99996948 12,71701323 12,71705163 12,71703243 1,53E-05 16 1,99996948 2 1,99998474 12,71703243 12,71705163 12,71704203 7,63E-06 17 1,99998474 2 1,99999237 12,71704203 12,71705163 12,71704683 3,81E-06 18 1,99999237 2 1,99999619 12,71704683 12,71705163 12,71704923 1,91E-06 19 1,99999619 2 1,99999809 12,71704923 12,71705163 12,71705043 9,54E-07 20 1,99999809 2 1,99999905 12,71705043 12,71705163 12,71705103 4,77E-07 21 1,99999905 2 1,99999952 12,71705103 12,71705163 12,71705133 2,38E-07 22 1,99999952 2 1,99999976 12,71705133 12,71705163 12,71705148 1,19E-07 Volume 8 No. 2 December 2022  Jurnal Pendidikan Fisika dan Teknologi (JPFT)    242 i a b c f(a) f(b) f(c) eror (ɛ) 23 1,99999976 2 1,99999988 12,71705148 12,71705163 12,71705156 5,96E-08 24 1,99999988 2 1,99999994 12,71705156 12,71705163 12,7170516 2,98E-08 25 1,99999994 2 1,99999997 12,7170516 12,71705163 12,71705161 1,49E-08 26 1,99999997 2 1,99999999 12,71705161 12,71705163 12,71705162 7,45E-09 27 1,99999999 2 1,99999999 12,71705162 12,71705163 12,71705163 3,73E-09 28 1,99999999 2 2 12,71705163 12,71705163 12,71705163 1,86E-09 29 2 2 2 12,71705163 12,71705163 12,71705163 9,31E-10 30 2 2 2 12,71705163 12,71705163 12,71705163 4,66E-10 31 2 2 2 12,71705163 12,71705163 12,71705163 2,33E-10 32 2 2 2 12,71705163 12,71705163 12,71705163 1,16E-10 33 2 2 2 12,71705163 12,71705163 12,71705163 5,82E-11 34 2 2 2 12,71705163 12,71705163 12,71705163 2,91E-11 35 2 2 2 12,71705163 12,71705163 12,71705163 1,46E-11 36 2 2 2 12,71705163 12,71705163 12,71705163 7,28E-12 37 2 2 2 12,71705163 12,71705163 12,71705163 3,64E-12 38 2 2 2 12,71705163 12,71705163 12,71705163 1,82E-12 39 2 2 2 12,71705163 12,71705163 12,71705163 9,09E-13 40 2 2 2 12,71705163 12,71705163 12,71705163 4,55E-13 41 2 2 2 12,71705163 12,71705163 12,71705163 2,27E-13 42 2 2 2 12,71705163 12,71705163 12,71705163 1,14E-13 43 2 2 2 12,71705163 12,71705163 12,71705163 5,68E-14 44 2 2 2 12,71705163 12,71705163 12,71705163 2,84E-14 45 2 2 2 12,71705163 12,71705163 12,71705163 1,42E-14 46 2 2 2 12,71705163 12,71705163 12,71705163 7,11E-15 47 2 2 2 12,71705163 12,71705163 12,71705163 3,55E-15 48 2 2 2 12,71705163 12,71705163 12,71705163 1,78E-15 49 2 2 2 12,71705163 12,71705163 12,71705163 8,88E-16 50 2 2 2 12,71705163 12,71705163 12,71705163 4,44E-16 51 2 2 2 12,71705163 12,71705163 12,71705163 2,22E-16 52 2 2 2 12,71705163 12,71705163 12,71705163 1,11E-16 53 2 2 2 12,71705163 12,71705163 12,71705163 1,11E-16 54 2 2 2 12,71705163 12,71705163 12,71705163 0 From the bisection numerical machine we can get the plot as follows:  Figure 2. Plots of functions against numbers (a,b, and c) in the geometric equations of temperature and humidity Volume 8 No. 2 December 2022  Jurnal Pendidikan Fisika dan Teknologi (JPFT)    243 And we can also see the error progress up to certain iterations, as seen below:  Figure 3. Eror data analysis Discussion In this sub-chapter we will explain the graphs that we have attached above. For Figure 1 is a graph that interprets the relationship between temperature and humidity in the city of Kuningan, West Java, where in the graph we can see that the graph of temperature has a linear correlation with humidity so that we can do a correlation with regression, from these 2 variables it can be processed the data to be used as a non-linear equation. The non-linear graph that we use is a geometric type. The next thing is if we have obtained data on variables x and y, which interpret humidity and temperature, then we can describe the data with logarithms, we must first get log a, log b, multiply log a and log b, square log a and square log b , and the amount of data, while the amount of data taken is 12 because it interprets 12 months in 1 year. After we get the log data, then we add up each data, for further processing. We get the value b, which is 0.098949483, from equation 5, we get the log a value from equation 4, where we process the log a to a value of a, which is 11.87407184 using the power rule, so the log is lost. So that's where we get the values of a and b, to be entered into the geometric equation variables. If we study the equations, of course we can process these equations into the bisection numerical method. The bisection method is a closed method for finding solutions to the roots of non-linear equations. In table 2 is the head table which we will process in the bisection numerical method. For machine programs in Exel to run as they should, then we can provide logic to Exel, namely evaluate using IF logic, where <f(a)*f(c)<0, then b=c, continue with the next step> , < f(a)*f(c)>0, then a=c, continue to the next step>, <f(a)*f(c)=0, stop iteration>. Next we may iterate until the iteration iteration for error is 0. After we do logic on the data, we can drag it so we get the value we want as shown in table 4. Figure 1 is an interpretation in table 4 which states the roots of the equation, from f(a) to f(b). For f(b) we take the numeric value is 2, and f(a) we take the numeric is 1, but the numeric does not have to have that value, we can also take the constraints randomly, depending on what we need in the method. Of course f(b) Volume 8 No. 2 December 2022  Jurnal Pendidikan Fisika dan Teknologi (JPFT)    244 will remain constant, while f(a) will approach f(b), so f(a) will be equal in value to f(b). Whereas f(c) is the middle value between f(a) and f(b), from this, f(c) will always be in the middle value between f(a) and f(b). Figure 3 is an error graph of f(a) and f(b), where the maximum data error is 0.15 from 0, and will decrease again per iteration or 50 repetitions.  CONCLUSION As for this paper, it has succeeded in explaining the bisection method for 2 nonlinear data using geometric equations. The data obtained uses real data for 2021 for the city of Kuningan, so that students can use this data to practice linear regression analysis and other numerical methods. In this paper, we explain non-linear regression teaching strategies and their relationship with the numerical bisection method with 2 different variables. This strategy is also expected to help lecturers and other researchers. It is suggested to the readers to develop 4 different numerical methods using the same data, and using real data from open access. It is also hoped that students or students will not only read theory, but can practice in other programming languages, such as Matlab, Python and so on.  REFERENCES Amemiya, T. (1983). Non-linear regression models. Handbook of Econometrics, 1, 333–389. Ayyub, B. M., & McCuen, R. H. (1995). Numerical methods for engineers. Prentice-Hall, Inc. Brook, R. J., & Arnold, G. C. (2018). Applied regression analysis and experimental design. CRC Press. Codau, T. C., Onofrei, E., Petrusic, S., Bedek, G., Dupont, D., & Soulat, D. (2015). Mathematical Correlation of Test Methods For Measuring Water-Vapor Transmission Through Fabrics. Journal of Porous Media, 18(3). Crosdale, P. J., Moore, T. A., & Mares, T. E. (2008). Influence of moisture content and temperature on methane adsorption isotherm analysis for coals from a low-rank, biogenically-sourced gas reservoir. International Journal of Coal Geology, 76(1–2), 166–174. Jumin, E., Basaruddin, F. B., Yusoff, Y. B., Latif, S. D., & Ahmed, A. N. (2021). Solar radiation prediction using boosted decision tree regression model: A case study in Malaysia. Environmental Science and Pollution Research, 28(21), 26571-26583. Pesaran, M. H., & Deaton, A. S. (1978). Testing non-nested nonlinear regression models. Econometrica: Journal of the Econometric Society, 677–694. Roberts, E. (1960). The viability of cereal seed in relation to temperature and moisture: With eight figures in the text. Annals of Botany, 24(1), 12–31. Zhao, Y., Wu, P., & Sun, W. (2014). Calculation of infrared system operating distance by spectral bisection method. Infrared Physics & Technology, 63, 198-203. 

Non-Linear Regresion And Bisection Method Numerical Analysis of Humidity And Temperature Relationships

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Non-Linear Regresion And Bisection Method Numerical Analysis of Humidity And Temperature Relationships

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